Solution - Simplification or other simple results
Step by Step Solution
Step 1 :
Equation at the end of step 1 :
((22•5x2) - 7x) - 40
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 20x2-7x-40
The first term is, 20x2 its coefficient is 20 .
The middle term is, -7x its coefficient is -7 .
The last term, "the constant", is -40
Step-1 : Multiply the coefficient of the first term by the constant 20 • -40 = -800
Step-2 : Find two factors of -800 whose sum equals the coefficient of the middle term, which is -7 .
| -800 | + | 1 | = | -799 | ||
| -400 | + | 2 | = | -398 | ||
| -200 | + | 4 | = | -196 | ||
| -160 | + | 5 | = | -155 | ||
| -100 | + | 8 | = | -92 | ||
| -80 | + | 10 | = | -70 | ||
| -50 | + | 16 | = | -34 | ||
| -40 | + | 20 | = | -20 | ||
| -32 | + | 25 | = | -7 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -32 and 25
20x2 - 32x + 25x - 40
Step-4 : Add up the first 2 terms, pulling out like factors :
4x • (5x-8)
Add up the last 2 terms, pulling out common factors :
5 • (5x-8)
Step-5 : Add up the four terms of step 4 :
(4x+5) • (5x-8)
Which is the desired factorization
Final result :
(5x - 8) • (4x + 5)
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